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serve_failure.py
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serve_failure.py
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from math import tau
import plotly.graph_objects as go
import numpy as np
def get_max_stress(s1, s2, t12, theta):
theta = np.radians(theta)
max_stress = tsai_hill_criterion(s1, s2, t12, theta)
return max_stress
def get_failure_mode(s1, s2, t12, theta):
theta = np.radians(theta)
modes = ['fibers', 'matrix', 'shear']
ms1 = max_sigma1_criterion(s1, theta)
ms2 = max_sigma2_criterion(s2, theta)
mt12 = max_shear_criterion(t12, theta)
mode = modes[np.argmin([ms1, ms2, mt12])]
return mode
def tsai_hill_criterion(sigma1, sigma2, tau12, t):
f_x = 1 / np.sqrt(
np.square(
np.cos(t)**2 / sigma1
) +
np.square(
np.sin(t)**2 / sigma2
) -
np.square(
np.sin(t) * np.cos(t) / sigma1
) +
np.square(
np.sin(t) * np.cos(t) / tau12
)
)
return f_x
def max_sigma1_criterion(sigma1, t):
f_x_1 = sigma1 / (np.cos(t)**2 + 1e-9)
return f_x_1
def max_sigma2_criterion(sigma2, t):
f_x_2 = sigma2 / (np.sin(t)**2 + 1e-9)
return f_x_2
def max_shear_criterion(tau12, t):
f_x_12 = tau12 / ((np.sin(t) * np.cos(t)) + 1e-9)
return f_x_12
def ply_failure_curves(sigma1, sigma2, tau12, thetas):
ply_failures_th = []
ply_failures_s1 = []
ply_failures_s2 = []
ply_failures_t12 = []
for t in thetas:
ply_failures_s1.append(
max_sigma1_criterion(sigma1, t)
)
ply_failures_s2.append(
max_sigma2_criterion(sigma2, t)
)
ply_failures_t12.append(
max_shear_criterion(tau12, t)
)
ply_failures_th.append(
tsai_hill_criterion(sigma1, sigma2, tau12, t)
)
return ply_failures_s1, ply_failures_s2, ply_failures_t12, ply_failures_th
def add_vrect_to_fig(fig, x0, x1, color):#, annotation):
fig.add_vrect(
x0=np.degrees(x0), x1=np.degrees(x1), fillcolor=color,
opacity=0.5, layer="below", line_width=0,
# annotation_text=annotation,
# annotation_position="bottom"
)
return fig
def add_failure_modes(fig, thetas, pfs1, pfs2, pft12):
colors = ['#f7f7f7', '#f7f7f7', '#fcfcfc']
# annotations = ['longitudinal strength limiting', 'transverse strength limiting', 'shear strength limiting']
x0 = thetas[0]
pad = (thetas[1] - thetas[0]) / 2
m0 = np.argmin([pfs1[0], pfs2[0], pft12[0]])
for t, fs1, fs2, ft12 in zip(thetas, pfs1, pfs2, pft12):
m = np.argmin([fs1, fs2, ft12])
if m != m0:
x1 = t
fig = add_vrect_to_fig(fig, x0 - pad, x1 - pad, colors[m0])#, annotations[m0])
x0 = x1
if t == thetas[-1]:
x1 = t
fig = add_vrect_to_fig(fig, x0 - pad, x1, colors[m0])#, annotations[m0])
m0 = m
return fig
def failure_wrapper(sigma1, sigma2, tau12):
thetas = np.radians(np.linspace(0, 90, 40))
pfs1, pfs2, pft12, pfth = ply_failure_curves(sigma1, sigma2, tau12, thetas)
fig = go.Figure()
fig.add_trace(go.Scatter(x=np.degrees(thetas), y=pfs1,
mode='lines',
name='Max \u03c3<sub>1</sub>',
line={ 'color': "#000000", 'dash': 'longdash' }
))
fig.add_trace(go.Scatter(x=np.degrees(thetas), y=pfs2,
mode='lines',
name='Max \u03c3<sub>2</sub>',
line={ 'color': "#000000", 'dash': 'dash' }
))
fig.add_trace(go.Scatter(x=np.degrees(thetas), y=pft12,
mode='lines',
name='Max \u03c4<sub>12</sub>',
line={ 'color': "#000000", 'dash': 'dot'}
))
fig.add_trace(go.Scatter(x=np.degrees(thetas), y=pfth,
mode='lines',
name='Tsai-Hill',
line={ 'color': "#000000" }
))
fig = add_failure_modes(fig, thetas, pfs1, pfs2, pft12)
fig.update_yaxes(range=[0, 2 * max(sigma1, sigma2)])
fig.update_xaxes(range=[0, 90], showgrid=False)
fig.update_layout(
xaxis_title=u"Theta (\u0398)",
yaxis_title="Stress [MPa]",
plot_bgcolor="#eeeeee",
)
return fig
if __name__ == '__main__':
fig = failure_wrapper(110, 60, 40)
fig.show()